Grinding blocks having a main body which has a framed receiving region with a recess for receiving a multiplicity of abrasive paper strips stood therein are known from the prior art. The main body has, on the bearing side, a groove-shaped indentation which fits together with a ridge on a supporting strip so that, in a mounted state, i.e. in a state in which the grinding block is screwed on, for example, a rotation of the grinding block as a workpiece is being processed is avoided by means of a form fit between the groove-shaped indentation on the underside of the grinding block and the matching ridge on the supporting strip, when the processing strip with a multiplicity of grinding blocks mounted thereupon is moved transversely to a workpiece.